Airy-averaged gradient corrections for two-dimensional fermion gases

作者：Trappe Martin I**jorn^*; Len Yink Loong; Ng Hui Khoon; Englert Berthold Georg

来源：Annals of Physics, 2017, 385: 136-161.

DOI：10.1016/j.aop.2017.07.020

• Orbital-free density-functional theory
• Gradient corrections
• Semiclassical expansions
• Single-particle density
• Kinetic energy functional
• Fermion gases

Building on the discussion in Trappe et al. (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading gradient corrections from a semiclassical expansion based on Wigner's phase space formalism and demonstrate that the semiclassical kinetic-energy density functional at zero temperature cannot be evaluated unambiguously. In contrast, a density-potential functional description that effectively incorporates interactions provides unambiguous gradient corrections. Employing an averaging procedure that involves Airy functions, thereby partially resumming higher-order gradient corrections, we facilitate a smooth transition of the particle density into the classically forbidden region of arbitrary smooth potentials. We find excellent agreement of the semiclassical Airy averaged particle densities with the exact densities for very low but finite temperatures, illustrated for a Fermi gas with harmonic potential energy. We furthermore provide criteria for the applicability of the semiclassical expansions at low temperatures. Finally, we derive a well-behaved ground-state kinetic-energy functional, which improves on the Thomas-Fermi approximation.

• 出版日期2017-10